Jerry Leiber and Mike Stoller all but wrote the book on creating radio-ready pop-rock; their songs, from “Hound Dog” to “Yakety Yak” to “Love Potion #9,” have more hooks than a chorus line of pirates.

No one, however, wrote the book for “Smokey Joe’s Cafe,” the theatrical ode to the influential songwriting duo. The Tony-winning 1995 show has no actual story, just 38 rapid-fire musical numbers, with occasionally the barest of narratives between them.

That revue format might not be everybody’s cup of java, but the “Cafe” that San Diego Musical Theatre is staging at the Lyceum downtown through this weekend proves a rousing jolt of good-time rock ’n’ roll just the same.

Credit director-choreographer Ron Kellum and his versatile, well-balanced cast of four women and five men. And give music director and conductor Don LeMaster his due, too, for leading the seven-piece band through the show’s 38 songs with plenty of pop and texture.

“Smokey Joe’s” does take a stab at a narrative framing device, opening with and reprising the wistful tune “Neighborhood.” There’s also a kind of call-and-response resonance between “Falling,” a torch-tune solo by the silky-voiced Lauren Hildebrandt, and “Ruby Baby,” a love-gone-wrong song that has the reliable Robert J. Townsend fronting the male ensemble.

Other songs need no story conceit to justify their presence: a bluesy take on “Hound Dog,” sung with soulful verve by Otha White; a suitably loopy performance of “Love Potion #9,” with Lawrence Cummings, Jay Donnell, David LaMarr and Dominic Rambaran; and an exhilarating swing through “On Broadway” with those same four.

Some lesser-known numbers get strong showcases, too: Laura Dickinson’s affecting solo on “Pearl’s a Singer,” and sultry Jenn Aedo’s turn on the sardonic “You’re the Boss” with Rambaran, whose arresting bass notes just about shake the Lyceum’s foundations.

Not everything works quite so well: The show’s “Kansas City” seems leached of conviction, and “D.W. Washburn,” with the cast decked out in straw boaters, feels as though it parachuted in from “The Music Man.”

But the one-two punch of “Spanish Harlem” and “I Who Have Nothing,” with a showstopping solo by Cummings, takes Act 2 into the home stretch impressively.

The show’s close brings the whole ensemble back onto the nightclub set — lit evocatively by Chris Rynne — for “Stand By Me,” the enduring hit co-composed by Leiber & Stoller and Ben E. King. It’s a stirring finish to a show that skips the plot but doesn’t skimp on simpler pleasures.